Gravitational Redshift and Dark Matter: Application to SO-2’s Case

Abstract

The star SO-2 at the galactic center will be soon at its closest distance to the supermassive black hole (SMBH). It will allow measuring relativistic effects. In [1] the dark matter is explained by the second component (gravitic field) of the general relativity generated by the clusters. In this theoretical frame, the gravitic field of the galaxies cannot explain the dark matter at their ends. But despite this, it seems possible that this gravitic field is in general underestimated. In the current paper, we study the component of the SO-2’s gravitational redshift due to the gravitic field of the galactic center (ZH) compared to the expected gravitational redshift due to the gravity field (ZG~3×10-4). The value of the gravitic field of SMBH is not known but depending on its value, four cases (in agreement with general relativity) can be obtained. If the discrepancy measured on the gravitational redshift of SO-2 is ZH~10-5, it will mean that the gravitic field at the center of the Galaxy is too weak to be measured and, as expected, that the gravity field dominates. If a discrepancy is measured of around ZH~10-5, the gravitic field at the Galaxy center will be greater than expected but always inferior to the effect of the gravity field. With a measure of around ZH~10-4, this discrepancy could always be explained in agreement with general relativity. It will mean that the effect of the gravitic field at the Galaxy center is greater than expected and can even be of the same order of magnitude than the effect of the gravity field. Furthermore the calculation of the mass could have to be revised. If a discrepancy is measured of around ZH~10-3 this discrepancy could always be explained in agreement with general relativity. It will mean that the effect of the gravitic field at the Galaxy center is greater than expected and even greater than the effect of the gravity field. The calculation of the mass will have to be revised. In the three previous cases, this discrepancy will be a measure of the gravitic field of SMBH and would be an important clue that would indirectly corroborate the explanation of the dark matter as the effect of the term of gravitic field. And to end, if the discrepancy is larger, it will be more difficult to explain it in the frame of the general relativity (even in the frame of the explanation of dark matter as the effect of the term of gravitic field).